After my first fiancee and then the girlfriend after her, cheated on me, I stopped trying to be Mr. Nice Guy and let the female have her way. I am a very alpha male who thought that women felt that alpha males were dumb jocks or jerks. Once I stopped pretending to be someone I wasn't, I had a lot of girlfriends who never cheated on me. I am married 44 years. One day my wife told me that she had feelings for someone else. I was expecting it to be a guy but it was a woman. She said that she only fantasizes about women and in particular, her best friend. She also said that she was conflicted and did not want to cheat. We found a solution that would not work if she had feelings for another guy. Long story short, we shared her girlfriend for most of our marriage.
We got a double whammy on the sterile side. Both of us are sterile so we never had kids. We do not mind because we had a lot of extra time and money to spoil ourselves and have a great lifestyle. From what we saw, having a kid sometimes drastically changes the relationship between husband and wife. You cannot miss what you never had.
The problem is that our emotions are governed by our brain and we feel what we feel due to a release of feel good hormones. No one knows why we are attracted to certain people and not others but once it happens, you cannot will the feelings to go away. They are either there or not. Even if your wife stops seeing the guy, her feelings will linger and perhaps make her unhappy in her marriage. You are in a difficult situation and perhaps she feels that she cannot share her emotions with you, which is why she feels that she has to go to someone else.
Men know that guys will do whatever it takes to have sex with a woman, even lending a sympathetic ear. So you have a real problem on your hands that you have to handle or let it play out. The problem with feelings is that it makes you overlook the other person's faults and only see the good. You want to be with that person as much as possible even if it means hurting someone else. That is why your wife is conflicted. Perhaps you are like me and not a very emotional person. That is one big reason why my wife needs a woman in her life. I am very logical and think with my brain. My wife thinks with her heart which I think is illogical.
The fact that your wife told you can mean two things. She could truly be conflicted and hope that by telling you, you will do something to stop her from having feelings for the other guy. You might suggest that she teaches dance for another company because things are not going to get better as long as she keeps seeing that guy.
The other thing could be is that she is letting you down easy so when she leaves you, it is not a big surprise and shock. I know how your wife feels because I once fell in love with one of the women I dated during my marriage. We obviously were nonmonogamous. I did not even like the other women much but I fell in love with her and could not stay away from her. I left my wife for a month until I came to my senses but even then, my love did not just go away because I wanted it to. The final solution for us was to move away and we did. That solved the problem. I got a job in another city as did my wife. We moved around a lot anyway for my business but this was one of two relocations we did to solve a problem in our marriage.
People do get addicted to other people and even though they know the sever consequences, will continue to see that other person. I know it first hand and have seen it with others. I wish you luck and perhaps you can examine your relationship and find a way to fix this problem.